Problem: Is ${459459}$ divisible by $4$ ?
A number is divisible by $4$ if the last two digits are divisible by $4$ . [ Why? We can rewrite the number as a multiple of $100$ plus the last two digits: $ \gray{4594} {59} = \gray{4594} \gray{00} + {59} $ Because $459400$ is a multiple of $100$ , it is also a multiple of $4$ So as long as the value of the last two digits, ${59}$ , is divisible by $4$ , the original number must also be divisible by $4$ Is the value of the last two digits, $59$ , divisible by $4$ No, $59$ is not divisible by $4$, so $459459$ is also not divisible by $4$.